Problem: Simplify the following expression: $r = \dfrac{k^2 - 12k + 27}{k - 9} $
Explanation: First factor the polynomial in the numerator. $ k^2 - 12k + 27 = (k - 9)(k - 3) $ So we can rewrite the expression as: $r = \dfrac{(k - 9)(k - 3)}{k - 9} $ We can divide the numerator and denominator by $(k - 9)$ on condition that $k \neq 9$ Therefore $r = k - 3; k \neq 9$